Stochastic differential equations are fundamental tools of modern mathematical modelling; they describe everything from the performance of financial instruments to atomic motion to the complex motion of fish schools or bird flocks. In recent years they have also been used increasingly as tools for the parameterization of artificial models such as neural networks in their application to analysis of data sets. Given their great relevance, it is obviously of crucial importance to design numerical methods having high efficiency (i.e. accuracy and stability) for solving stochastic systems. I will describe a number of examples of stochastic differential equations arising in applications, while also presenting a few principles for the construction of high quality numerical methods for their computational treatment.
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Conference in Honor of the 70th Birthday of Tudor Ratiu, 20 to 24 July 2020.
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